PA and PB are tangents to the circle drawn from an external point P. CD is the 3rd tangent touching the circle at Q. If PA = 15cm, find the perimeter of ⊿PCD.
Answers
Given : PA and PB are tangents to the circle drawn from an external point P. CD is the 3rd tangent touching the circle at Q. PA = 15cm
To Find : the perimeter of ⊿PCD.
Solution:
Perimeter of triangle PCD
PC + CD + PD
CD = CQ + DQ
=> Perimeter of triangle PCD = PC + CQ + DQ + PD
CQ = CA Equal tangent
DQ = DB Equal tangent
=> Perimeter of triangle PCD = PC + CA + DB + PD
PC + CA = PA
DB + PD = PB
=> Perimeter of triangle PCD = PA + PB
PA = PB Equal tangent
=> Perimeter of triangle PCD = PA + PA
=> Perimeter of triangle PCD = 2 * PA
PA = 15 cm
=> Perimeter of triangle PCD = 2 * 15 = 30 cm
Perimeter of triangle PCD = 30 cm
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